// This file is part of Eigen, a lightweight C++ template library
// for linear algebra.
//
// Copyright (C) 2009-2010 Gael Guennebaud <gael.guennebaud@inria.fr>
//
// This Source Code Form is subject to the terms of the Mozilla
// Public License v. 2.0. If a copy of the MPL was not distributed
// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.

#ifndef EIGEN_BLASUTIL_H
#define EIGEN_BLASUTIL_H

// This file contains many lightweight helper classes used to
// implement and control fast level 2 and level 3 BLAS-like routines.

namespace Eigen {

namespace internal {

// forward declarations
template<typename LhsScalar,
		 typename RhsScalar,
		 typename Index,
		 typename DataMapper,
		 int mr,
		 int nr,
		 bool ConjugateLhs = false,
		 bool ConjugateRhs = false>
struct gebp_kernel;

template<typename Scalar,
		 typename Index,
		 typename DataMapper,
		 int nr,
		 int StorageOrder,
		 bool Conjugate = false,
		 bool PanelMode = false>
struct gemm_pack_rhs;

template<typename Scalar,
		 typename Index,
		 typename DataMapper,
		 int Pack1,
		 int Pack2,
		 typename Packet,
		 int StorageOrder,
		 bool Conjugate = false,
		 bool PanelMode = false>
struct gemm_pack_lhs;

template<typename Index,
		 typename LhsScalar,
		 int LhsStorageOrder,
		 bool ConjugateLhs,
		 typename RhsScalar,
		 int RhsStorageOrder,
		 bool ConjugateRhs,
		 int ResStorageOrder,
		 int ResInnerStride>
struct general_matrix_matrix_product;

template<typename Index,
		 typename LhsScalar,
		 typename LhsMapper,
		 int LhsStorageOrder,
		 bool ConjugateLhs,
		 typename RhsScalar,
		 typename RhsMapper,
		 bool ConjugateRhs,
		 int Version = Specialized>
struct general_matrix_vector_product;

template<typename From, typename To>
struct get_factor
{
	EIGEN_DEVICE_FUNC static EIGEN_STRONG_INLINE To run(const From& x) { return To(x); }
};

template<typename Scalar>
struct get_factor<Scalar, typename NumTraits<Scalar>::Real>
{
	EIGEN_DEVICE_FUNC
	static EIGEN_STRONG_INLINE typename NumTraits<Scalar>::Real run(const Scalar& x) { return numext::real(x); }
};

template<typename Scalar, typename Index>
class BlasVectorMapper
{
  public:
	EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE BlasVectorMapper(Scalar* data)
		: m_data(data)
	{
	}

	EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE Scalar operator()(Index i) const { return m_data[i]; }
	template<typename Packet, int AlignmentType>
	EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE Packet load(Index i) const
	{
		return ploadt<Packet, AlignmentType>(m_data + i);
	}

	template<typename Packet>
	EIGEN_DEVICE_FUNC bool aligned(Index i) const
	{
		return (UIntPtr(m_data + i) % sizeof(Packet)) == 0;
	}

  protected:
	Scalar* m_data;
};

template<typename Scalar, typename Index, int AlignmentType, int Incr = 1>
class BlasLinearMapper;

template<typename Scalar, typename Index, int AlignmentType>
class BlasLinearMapper<Scalar, Index, AlignmentType>
{
  public:
	EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE BlasLinearMapper(Scalar* data, Index incr = 1)
		: m_data(data)
	{
		EIGEN_ONLY_USED_FOR_DEBUG(incr);
		eigen_assert(incr == 1);
	}

	EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE void prefetch(int i) const { internal::prefetch(&operator()(i)); }

	EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE Scalar& operator()(Index i) const { return m_data[i]; }

	template<typename PacketType>
	EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE PacketType loadPacket(Index i) const
	{
		return ploadt<PacketType, AlignmentType>(m_data + i);
	}

	template<typename PacketType>
	EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE void storePacket(Index i, const PacketType& p) const
	{
		pstoret<Scalar, PacketType, AlignmentType>(m_data + i, p);
	}

  protected:
	Scalar* m_data;
};

// Lightweight helper class to access matrix coefficients.
template<typename Scalar, typename Index, int StorageOrder, int AlignmentType = Unaligned, int Incr = 1>
class blas_data_mapper;

// TMP to help PacketBlock store implementation.
// There's currently no known use case for PacketBlock load.
// The default implementation assumes ColMajor order.
// It always store each packet sequentially one `stride` apart.
template<typename Index, typename Scalar, typename Packet, int n, int idx, int StorageOrder>
struct PacketBlockManagement
{
	PacketBlockManagement<Index, Scalar, Packet, n, idx - 1, StorageOrder> pbm;
	EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE void store(Scalar* to,
													 const Index stride,
													 Index i,
													 Index j,
													 const PacketBlock<Packet, n>& block) const
	{
		pbm.store(to, stride, i, j, block);
		pstoreu<Scalar>(to + i + (j + idx) * stride, block.packet[idx]);
	}
};

// PacketBlockManagement specialization to take care of RowMajor order without ifs.
template<typename Index, typename Scalar, typename Packet, int n, int idx>
struct PacketBlockManagement<Index, Scalar, Packet, n, idx, RowMajor>
{
	PacketBlockManagement<Index, Scalar, Packet, n, idx - 1, RowMajor> pbm;
	EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE void store(Scalar* to,
													 const Index stride,
													 Index i,
													 Index j,
													 const PacketBlock<Packet, n>& block) const
	{
		pbm.store(to, stride, i, j, block);
		pstoreu<Scalar>(to + j + (i + idx) * stride, block.packet[idx]);
	}
};

template<typename Index, typename Scalar, typename Packet, int n, int StorageOrder>
struct PacketBlockManagement<Index, Scalar, Packet, n, -1, StorageOrder>
{
	EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE void store(Scalar* to,
													 const Index stride,
													 Index i,
													 Index j,
													 const PacketBlock<Packet, n>& block) const
	{
		EIGEN_UNUSED_VARIABLE(to);
		EIGEN_UNUSED_VARIABLE(stride);
		EIGEN_UNUSED_VARIABLE(i);
		EIGEN_UNUSED_VARIABLE(j);
		EIGEN_UNUSED_VARIABLE(block);
	}
};

template<typename Index, typename Scalar, typename Packet, int n>
struct PacketBlockManagement<Index, Scalar, Packet, n, -1, RowMajor>
{
	EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE void store(Scalar* to,
													 const Index stride,
													 Index i,
													 Index j,
													 const PacketBlock<Packet, n>& block) const
	{
		EIGEN_UNUSED_VARIABLE(to);
		EIGEN_UNUSED_VARIABLE(stride);
		EIGEN_UNUSED_VARIABLE(i);
		EIGEN_UNUSED_VARIABLE(j);
		EIGEN_UNUSED_VARIABLE(block);
	}
};

template<typename Scalar, typename Index, int StorageOrder, int AlignmentType>
class blas_data_mapper<Scalar, Index, StorageOrder, AlignmentType, 1>
{
  public:
	typedef BlasLinearMapper<Scalar, Index, AlignmentType> LinearMapper;
	typedef BlasVectorMapper<Scalar, Index> VectorMapper;

	EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE blas_data_mapper(Scalar* data, Index stride, Index incr = 1)
		: m_data(data)
		, m_stride(stride)
	{
		EIGEN_ONLY_USED_FOR_DEBUG(incr);
		eigen_assert(incr == 1);
	}

	EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE blas_data_mapper<Scalar, Index, StorageOrder, AlignmentType> getSubMapper(
		Index i,
		Index j) const
	{
		return blas_data_mapper<Scalar, Index, StorageOrder, AlignmentType>(&operator()(i, j), m_stride);
	}

	EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE LinearMapper getLinearMapper(Index i, Index j) const
	{
		return LinearMapper(&operator()(i, j));
	}

	EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE VectorMapper getVectorMapper(Index i, Index j) const
	{
		return VectorMapper(&operator()(i, j));
	}

	EIGEN_DEVICE_FUNC
	EIGEN_ALWAYS_INLINE Scalar& operator()(Index i, Index j) const
	{
		return m_data[StorageOrder == RowMajor ? j + i * m_stride : i + j * m_stride];
	}

	template<typename PacketType>
	EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE PacketType loadPacket(Index i, Index j) const
	{
		return ploadt<PacketType, AlignmentType>(&operator()(i, j));
	}

	template<typename PacketT, int AlignmentT>
	EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE PacketT load(Index i, Index j) const
	{
		return ploadt<PacketT, AlignmentT>(&operator()(i, j));
	}

	template<typename SubPacket>
	EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE void scatterPacket(Index i, Index j, const SubPacket& p) const
	{
		pscatter<Scalar, SubPacket>(&operator()(i, j), p, m_stride);
	}

	template<typename SubPacket>
	EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE SubPacket gatherPacket(Index i, Index j) const
	{
		return pgather<Scalar, SubPacket>(&operator()(i, j), m_stride);
	}

	EIGEN_DEVICE_FUNC const Index stride() const { return m_stride; }
	EIGEN_DEVICE_FUNC const Scalar* data() const { return m_data; }

	EIGEN_DEVICE_FUNC Index firstAligned(Index size) const
	{
		if (UIntPtr(m_data) % sizeof(Scalar)) {
			return -1;
		}
		return internal::first_default_aligned(m_data, size);
	}

	template<typename SubPacket, int n>
	EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE void storePacketBlock(Index i,
																Index j,
																const PacketBlock<SubPacket, n>& block) const
	{
		PacketBlockManagement<Index, Scalar, SubPacket, n, n - 1, StorageOrder> pbm;
		pbm.store(m_data, m_stride, i, j, block);
	}

  protected:
	Scalar* EIGEN_RESTRICT m_data;
	const Index m_stride;
};

// Implementation of non-natural increment (i.e. inner-stride != 1)
// The exposed API is not complete yet compared to the Incr==1 case
// because some features makes less sense in this case.
template<typename Scalar, typename Index, int AlignmentType, int Incr>
class BlasLinearMapper
{
  public:
	EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE BlasLinearMapper(Scalar* data, Index incr)
		: m_data(data)
		, m_incr(incr)
	{
	}

	EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE void prefetch(int i) const { internal::prefetch(&operator()(i)); }

	EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE Scalar& operator()(Index i) const { return m_data[i * m_incr.value()]; }

	template<typename PacketType>
	EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE PacketType loadPacket(Index i) const
	{
		return pgather<Scalar, PacketType>(m_data + i * m_incr.value(), m_incr.value());
	}

	template<typename PacketType>
	EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE void storePacket(Index i, const PacketType& p) const
	{
		pscatter<Scalar, PacketType>(m_data + i * m_incr.value(), p, m_incr.value());
	}

  protected:
	Scalar* m_data;
	const internal::variable_if_dynamic<Index, Incr> m_incr;
};

template<typename Scalar, typename Index, int StorageOrder, int AlignmentType, int Incr>
class blas_data_mapper
{
  public:
	typedef BlasLinearMapper<Scalar, Index, AlignmentType, Incr> LinearMapper;

	EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE blas_data_mapper(Scalar* data, Index stride, Index incr)
		: m_data(data)
		, m_stride(stride)
		, m_incr(incr)
	{
	}

	EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE blas_data_mapper getSubMapper(Index i, Index j) const
	{
		return blas_data_mapper(&operator()(i, j), m_stride, m_incr.value());
	}

	EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE LinearMapper getLinearMapper(Index i, Index j) const
	{
		return LinearMapper(&operator()(i, j), m_incr.value());
	}

	EIGEN_DEVICE_FUNC
	EIGEN_ALWAYS_INLINE Scalar& operator()(Index i, Index j) const
	{
		return m_data[StorageOrder == RowMajor ? j * m_incr.value() + i * m_stride : i * m_incr.value() + j * m_stride];
	}

	template<typename PacketType>
	EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE PacketType loadPacket(Index i, Index j) const
	{
		return pgather<Scalar, PacketType>(&operator()(i, j), m_incr.value());
	}

	template<typename PacketT, int AlignmentT>
	EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE PacketT load(Index i, Index j) const
	{
		return pgather<Scalar, PacketT>(&operator()(i, j), m_incr.value());
	}

	template<typename SubPacket>
	EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE void scatterPacket(Index i, Index j, const SubPacket& p) const
	{
		pscatter<Scalar, SubPacket>(&operator()(i, j), p, m_stride);
	}

	template<typename SubPacket>
	EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE SubPacket gatherPacket(Index i, Index j) const
	{
		return pgather<Scalar, SubPacket>(&operator()(i, j), m_stride);
	}

	// storePacketBlock_helper defines a way to access values inside the PacketBlock, this is essentially required by
	// the Complex types.
	template<typename SubPacket, typename ScalarT, int n, int idx>
	struct storePacketBlock_helper
	{
		storePacketBlock_helper<SubPacket, ScalarT, n, idx - 1> spbh;
		EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE void store(
			const blas_data_mapper<Scalar, Index, StorageOrder, AlignmentType, Incr>* sup,
			Index i,
			Index j,
			const PacketBlock<SubPacket, n>& block) const
		{
			spbh.store(sup, i, j, block);
			for (int l = 0; l < unpacket_traits<SubPacket>::size; l++) {
				ScalarT* v = &sup->operator()(i + l, j + idx);
				*v = block.packet[idx][l];
			}
		}
	};

	template<typename SubPacket, int n, int idx>
	struct storePacketBlock_helper<SubPacket, std::complex<float>, n, idx>
	{
		storePacketBlock_helper<SubPacket, std::complex<float>, n, idx - 1> spbh;
		EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE void store(
			const blas_data_mapper<Scalar, Index, StorageOrder, AlignmentType, Incr>* sup,
			Index i,
			Index j,
			const PacketBlock<SubPacket, n>& block) const
		{
			spbh.store(sup, i, j, block);
			for (int l = 0; l < unpacket_traits<SubPacket>::size; l++) {
				std::complex<float>* v = &sup->operator()(i + l, j + idx);
				v->real(block.packet[idx].v[2 * l + 0]);
				v->imag(block.packet[idx].v[2 * l + 1]);
			}
		}
	};

	template<typename SubPacket, int n, int idx>
	struct storePacketBlock_helper<SubPacket, std::complex<double>, n, idx>
	{
		storePacketBlock_helper<SubPacket, std::complex<double>, n, idx - 1> spbh;
		EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE void store(
			const blas_data_mapper<Scalar, Index, StorageOrder, AlignmentType, Incr>* sup,
			Index i,
			Index j,
			const PacketBlock<SubPacket, n>& block) const
		{
			spbh.store(sup, i, j, block);
			for (int l = 0; l < unpacket_traits<SubPacket>::size; l++) {
				std::complex<double>* v = &sup->operator()(i + l, j + idx);
				v->real(block.packet[idx].v[2 * l + 0]);
				v->imag(block.packet[idx].v[2 * l + 1]);
			}
		}
	};

	template<typename SubPacket, typename ScalarT, int n>
	struct storePacketBlock_helper<SubPacket, ScalarT, n, -1>
	{
		EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE void store(
			const blas_data_mapper<Scalar, Index, StorageOrder, AlignmentType, Incr>*,
			Index,
			Index,
			const PacketBlock<SubPacket, n>&) const
		{
		}
	};

	template<typename SubPacket, int n>
	struct storePacketBlock_helper<SubPacket, std::complex<float>, n, -1>
	{
		EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE void store(
			const blas_data_mapper<Scalar, Index, StorageOrder, AlignmentType, Incr>*,
			Index,
			Index,
			const PacketBlock<SubPacket, n>&) const
		{
		}
	};

	template<typename SubPacket, int n>
	struct storePacketBlock_helper<SubPacket, std::complex<double>, n, -1>
	{
		EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE void store(
			const blas_data_mapper<Scalar, Index, StorageOrder, AlignmentType, Incr>*,
			Index,
			Index,
			const PacketBlock<SubPacket, n>&) const
		{
		}
	};
	// This function stores a PacketBlock on m_data, this approach is really quite slow compare to Incr=1 and should be
	// avoided when possible.
	template<typename SubPacket, int n>
	EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE void storePacketBlock(Index i,
																Index j,
																const PacketBlock<SubPacket, n>& block) const
	{
		storePacketBlock_helper<SubPacket, Scalar, n, n - 1> spb;
		spb.store(this, i, j, block);
	}

  protected:
	Scalar* EIGEN_RESTRICT m_data;
	const Index m_stride;
	const internal::variable_if_dynamic<Index, Incr> m_incr;
};

// lightweight helper class to access matrix coefficients (const version)
template<typename Scalar, typename Index, int StorageOrder>
class const_blas_data_mapper : public blas_data_mapper<const Scalar, Index, StorageOrder>
{
  public:
	EIGEN_ALWAYS_INLINE const_blas_data_mapper(const Scalar* data, Index stride)
		: blas_data_mapper<const Scalar, Index, StorageOrder>(data, stride)
	{
	}

	EIGEN_ALWAYS_INLINE const_blas_data_mapper<Scalar, Index, StorageOrder> getSubMapper(Index i, Index j) const
	{
		return const_blas_data_mapper<Scalar, Index, StorageOrder>(&(this->operator()(i, j)), this->m_stride);
	}
};

/* Helper class to analyze the factors of a Product expression.
 * In particular it allows to pop out operator-, scalar multiples,
 * and conjugate */
template<typename XprType>
struct blas_traits
{
	typedef typename traits<XprType>::Scalar Scalar;
	typedef const XprType& ExtractType;
	typedef XprType _ExtractType;
	enum
	{
		IsComplex = NumTraits<Scalar>::IsComplex,
		IsTransposed = false,
		NeedToConjugate = false,
		HasUsableDirectAccess =
			((int(XprType::Flags) & DirectAccessBit) &&
			 (bool(XprType::IsVectorAtCompileTime) || int(inner_stride_at_compile_time<XprType>::ret) == 1))
				? 1
				: 0,
		HasScalarFactor = false
	};
	typedef typename conditional<bool(HasUsableDirectAccess), ExtractType, typename _ExtractType::PlainObject>::type
		DirectLinearAccessType;
	static inline EIGEN_DEVICE_FUNC ExtractType extract(const XprType& x) { return x; }
	static inline EIGEN_DEVICE_FUNC const Scalar extractScalarFactor(const XprType&) { return Scalar(1); }
};

// pop conjugate
template<typename Scalar, typename NestedXpr>
struct blas_traits<CwiseUnaryOp<scalar_conjugate_op<Scalar>, NestedXpr>> : blas_traits<NestedXpr>
{
	typedef blas_traits<NestedXpr> Base;
	typedef CwiseUnaryOp<scalar_conjugate_op<Scalar>, NestedXpr> XprType;
	typedef typename Base::ExtractType ExtractType;

	enum
	{
		IsComplex = NumTraits<Scalar>::IsComplex,
		NeedToConjugate = Base::NeedToConjugate ? 0 : IsComplex
	};
	static inline ExtractType extract(const XprType& x) { return Base::extract(x.nestedExpression()); }
	static inline Scalar extractScalarFactor(const XprType& x)
	{
		return conj(Base::extractScalarFactor(x.nestedExpression()));
	}
};

// pop scalar multiple
template<typename Scalar, typename NestedXpr, typename Plain>
struct blas_traits<
	CwiseBinaryOp<scalar_product_op<Scalar>, const CwiseNullaryOp<scalar_constant_op<Scalar>, Plain>, NestedXpr>>
	: blas_traits<NestedXpr>
{
	enum
	{
		HasScalarFactor = true
	};
	typedef blas_traits<NestedXpr> Base;
	typedef CwiseBinaryOp<scalar_product_op<Scalar>, const CwiseNullaryOp<scalar_constant_op<Scalar>, Plain>, NestedXpr>
		XprType;
	typedef typename Base::ExtractType ExtractType;
	static inline EIGEN_DEVICE_FUNC ExtractType extract(const XprType& x) { return Base::extract(x.rhs()); }
	static inline EIGEN_DEVICE_FUNC Scalar extractScalarFactor(const XprType& x)
	{
		return x.lhs().functor().m_other * Base::extractScalarFactor(x.rhs());
	}
};
template<typename Scalar, typename NestedXpr, typename Plain>
struct blas_traits<
	CwiseBinaryOp<scalar_product_op<Scalar>, NestedXpr, const CwiseNullaryOp<scalar_constant_op<Scalar>, Plain>>>
	: blas_traits<NestedXpr>
{
	enum
	{
		HasScalarFactor = true
	};
	typedef blas_traits<NestedXpr> Base;
	typedef CwiseBinaryOp<scalar_product_op<Scalar>, NestedXpr, const CwiseNullaryOp<scalar_constant_op<Scalar>, Plain>>
		XprType;
	typedef typename Base::ExtractType ExtractType;
	static inline ExtractType extract(const XprType& x) { return Base::extract(x.lhs()); }
	static inline Scalar extractScalarFactor(const XprType& x)
	{
		return Base::extractScalarFactor(x.lhs()) * x.rhs().functor().m_other;
	}
};
template<typename Scalar, typename Plain1, typename Plain2>
struct blas_traits<CwiseBinaryOp<scalar_product_op<Scalar>,
								 const CwiseNullaryOp<scalar_constant_op<Scalar>, Plain1>,
								 const CwiseNullaryOp<scalar_constant_op<Scalar>, Plain2>>>
	: blas_traits<CwiseNullaryOp<scalar_constant_op<Scalar>, Plain1>>
{};

// pop opposite
template<typename Scalar, typename NestedXpr>
struct blas_traits<CwiseUnaryOp<scalar_opposite_op<Scalar>, NestedXpr>> : blas_traits<NestedXpr>
{
	enum
	{
		HasScalarFactor = true
	};
	typedef blas_traits<NestedXpr> Base;
	typedef CwiseUnaryOp<scalar_opposite_op<Scalar>, NestedXpr> XprType;
	typedef typename Base::ExtractType ExtractType;
	static inline ExtractType extract(const XprType& x) { return Base::extract(x.nestedExpression()); }
	static inline Scalar extractScalarFactor(const XprType& x)
	{
		return -Base::extractScalarFactor(x.nestedExpression());
	}
};

// pop/push transpose
template<typename NestedXpr>
struct blas_traits<Transpose<NestedXpr>> : blas_traits<NestedXpr>
{
	typedef typename NestedXpr::Scalar Scalar;
	typedef blas_traits<NestedXpr> Base;
	typedef Transpose<NestedXpr> XprType;
	typedef Transpose<const typename Base::_ExtractType>
		ExtractType; // const to get rid of a compile error; anyway blas traits are only used on the RHS
	typedef Transpose<const typename Base::_ExtractType> _ExtractType;
	typedef
		typename conditional<bool(Base::HasUsableDirectAccess), ExtractType, typename ExtractType::PlainObject>::type
			DirectLinearAccessType;
	enum
	{
		IsTransposed = Base::IsTransposed ? 0 : 1
	};
	static inline ExtractType extract(const XprType& x) { return ExtractType(Base::extract(x.nestedExpression())); }
	static inline Scalar extractScalarFactor(const XprType& x)
	{
		return Base::extractScalarFactor(x.nestedExpression());
	}
};

template<typename T>
struct blas_traits<const T> : blas_traits<T>
{};

template<typename T, bool HasUsableDirectAccess = blas_traits<T>::HasUsableDirectAccess>
struct extract_data_selector
{
	EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE static const typename T::Scalar* run(const T& m)
	{
		return blas_traits<T>::extract(m).data();
	}
};

template<typename T>
struct extract_data_selector<T, false>
{
	static typename T::Scalar* run(const T&) { return 0; }
};

template<typename T>
EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE const typename T::Scalar*
extract_data(const T& m)
{
	return extract_data_selector<T>::run(m);
}

/**
 * \c combine_scalar_factors extracts and multiplies factors from GEMM and GEMV products.
 * There is a specialization for booleans
 */
template<typename ResScalar, typename Lhs, typename Rhs>
struct combine_scalar_factors_impl
{
	EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE static ResScalar run(const Lhs& lhs, const Rhs& rhs)
	{
		return blas_traits<Lhs>::extractScalarFactor(lhs) * blas_traits<Rhs>::extractScalarFactor(rhs);
	}
	EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE static ResScalar run(const ResScalar& alpha, const Lhs& lhs, const Rhs& rhs)
	{
		return alpha * blas_traits<Lhs>::extractScalarFactor(lhs) * blas_traits<Rhs>::extractScalarFactor(rhs);
	}
};
template<typename Lhs, typename Rhs>
struct combine_scalar_factors_impl<bool, Lhs, Rhs>
{
	EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE static bool run(const Lhs& lhs, const Rhs& rhs)
	{
		return blas_traits<Lhs>::extractScalarFactor(lhs) && blas_traits<Rhs>::extractScalarFactor(rhs);
	}
	EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE static bool run(const bool& alpha, const Lhs& lhs, const Rhs& rhs)
	{
		return alpha && blas_traits<Lhs>::extractScalarFactor(lhs) && blas_traits<Rhs>::extractScalarFactor(rhs);
	}
};

template<typename ResScalar, typename Lhs, typename Rhs>
EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE ResScalar
combine_scalar_factors(const ResScalar& alpha, const Lhs& lhs, const Rhs& rhs)
{
	return combine_scalar_factors_impl<ResScalar, Lhs, Rhs>::run(alpha, lhs, rhs);
}
template<typename ResScalar, typename Lhs, typename Rhs>
EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE ResScalar
combine_scalar_factors(const Lhs& lhs, const Rhs& rhs)
{
	return combine_scalar_factors_impl<ResScalar, Lhs, Rhs>::run(lhs, rhs);
}

} // end namespace internal

} // end namespace Eigen

#endif // EIGEN_BLASUTIL_H
